Given an ordinary projective surface \(S\)  in the projective space \(P^3\)  over a number field, if \(S\)  is birationally equivalent to a rational surface, the software Magma [1]} determines the map to such a rational surface and returns its type within five categories. The returned type of \(S\)  is \(P^2\)  for the projective plane, a quadric surface (for a degree 2 surface in \(P^3\) ), a rational ruled surface, a conic bundle or a degree \(p\)  Del Pezzo surface where \(1 \le p \le 9\) .
